I just assume that the warp field makes a crazy visual distortion that makes stars appear to move faster than they are actually moving. The stars are swirling around the warp bubble (that the ship creates) in a weird, illogical manner where some stars that have already passed the vessel are visible in the front of the ship, and vice versa.

I think some sort of optical illusion would be absolutely expected - after all , we can't even watch the spokes on a wheel turning beyond a certain speed without them seeming to run backwards, and that's much slower that lightspeed. The human eye (and brain) was just not built to interpret FTL velocities.